Suzuki tied it 2-2 at 8:18 when he scored on his rebound.
Cam Atkinson scored to make it 3-2 at 2:41 of the third period.
Montembeault made six saves to keep the Canadiens in the game, and said he appreciated the trust the coaching staff showed in him.
"It was a long game too on Saturday so it's fun to see that the coaches trust me to go out on a back to back like that," he said. "I was really happy and I played a great game."
The Flyers had a power play when Chris Wideman was called for interference at 19:00, but they lost a face-off in the Canadiens zone, and the play ended with Pitlick scoring the tying goal.
"Right now, we're in a deep hole," Giroux said. "We're just finding ways to lose right now. Our whole game we played pretty solid, had a lot of chances, did a lot of good things. End of the game we always find a way to lose the game."